in Chemical Comlinations. 115 



mav not have re-entering angles. This polyhedron only differs 

 from the hexa-tetrahedron in having, besides the latter, regular 

 pyramids raised on its square faces. I shall call it a pyraniidated 

 hexa-tetrahedron. 



We may also combine the liexa-tctrahedron with a cube, by 

 uniting it to the verv cube which has served for its construction. 

 Tlie polyhedron which results from this combination being 

 formed by the union of a cube and a hexa-tetrahedron, I gave it 

 the name of cube-hexa-tetrahedron ; it has 32 summits and 

 54 faces; viz. six squares, and 48 isosceles triangles. 



If we prolong in this polyhedron the plans of the twenty-four 

 triangular faces adjacent to the square faces on the side where 

 they join those faces, until they cut each other by fours outside 

 of the polyhedron opposite to those squares, we shall obtain a 

 new representative form, produced by the union of a hexa-tetra- 

 hedron, a cube, and an octohedron v/hich will have .'58 sum- 

 mits and 48 faces, the half of which will be equal rhombs, and 

 the other half isosceles triangles also equal among each other. 

 In order to designate it by a name derived from tins property, 

 which distinguishes it from all the other representative forms in 

 whicli we find at once tetrahedrons and octohedrons, I shall call it 

 amphihedron. 



In order to form a simple idea of the combination of the 

 hexa-tetrahedron with a hexahedral prism formed by the union 

 of two regular octohedrons, we shall conceive the hexa-tctrii- 

 hedron placed in such a way that two of its hexagonal faces shall 

 be horizontal, when the middles of its six square faces will be 

 placed as the six summits of one of the octoh.edrons of which 

 the prism is composed. We may then place those six summits 

 on the perpendiculars elevated in the midst of these faces. The 

 six other summits of the hexahedral prism will answer to the 

 six hexagonal faces of the hexa-tetrahedron different from tjiose 

 which we have placed horizontally, i. e. in a direction perpendi- 

 cular to the axis of the prism. If we determine the respective 

 dimensions of the two polyhedrons, so that each side of the bases 

 of the prism shall meet the ridge of the hexa-tetrahedron, which 

 separates those of its faces to which the two extremities of this 

 side answer, we shall obtain a representative form composed 

 of six tetrahedrons and tv/o octohedrons which will have 36 

 tiummits and 50 faces ; viz. tv.-o hexagons similar to those ot 

 the hexa-tetrahedron, 12 quadrilaterals, 24 isosceles triangles, 

 and 12 scalene triangles. I shall give it the name of pentaconta- 

 liedron. 



In order to unite a hexa-tetrahedron with a trioctohedron, it 



is j^uflicient to place one of the three octohedrons of which the 



latter is composed in the same, way as the octohedron which we 



112 have 



